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Question

If x5(1+x3)2/3dx=A(1+x3)8/3+B(1+x3)5/3+c, then

A
A=14,B=15
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B
A=18,B=15
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C
A=18,B=15
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D
None of these
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Solution

The correct option is B A=14,B=15
x5(1+x3)2/3dx

Let x3=t 3x2dx=dt

=x3x2(1+x3)2/3dx

=t(1+t)2/3dt3

=13[t(1+t)2/3dtdtdt((1+t)2/3dt)dt]

=13[t(1+t)5/35/3(1+t)5/35/3dt]

=13[3t5(1+t)5/335(1+t)8/38/3]

=t(1+t)5/35340(1+t)8/3

So, A=340

=x3(1+x3)5/35340(1+x3)8/3

B=15 (Answer)

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